1. Field of the Invention
This invention generally relates to an optical low pass filter and, more particularly, to an optical low pass filter for use with an image sensing device, for example, a solid state image sensing device using a CCD (charge coupled device), an MOS (metal oxide semiconductor) device and the like which produces a predetermined image pickup output by carrying out the spatial sampling in two dimensions.
2. Description of the Prior Art
A color image pickup apparatus, or a color video camera using, for example, a CCD as the solid state image sensing device thereof is arranged to produce a predetermined color video output by sampling a color analyzed image of an object obtained through a color filter that is disposed at the front of the video camera.
In the image sensing system which produces a color signal by carrying out the color coding by the color filter and the spatial sampling at each color, it is well known that, based upon the side band component which is caused by the fact that sampling carrier is modulated by the sampling frequency component upon the sampling, an aliasing distortion will be produced. The generation of the carrier component which will cause such aliasing distortion is different dependent on the color coding.
FIG. 1A is a diagram showing an example of the alignment of picture elements of one-chip CCD image sensor 1 and the opening portion thereof. In FIG. 1A, reference numeral 2 designates the picture element of the image sensor 1, reference letter H designates the horizontal scanning direction thereof, reference letter V designates the vertical scanning direction thereof, reference letter Px designates an opening width in the horizontal direction of the CCD image sensor 1 and reference letter Py designates an opening width in the vertical direction thereof. When a color filter 3 in which 3 of longitudinal stripe-shape color filter elements of three primary colors R (red), G (green) and B (blue) are repeated as shown in FIG. 1B is used for the image sensor 1, carrier components, which will be mentioned below, will be generated.
The spatial sampling in the horizontal direction of Px and in the vertical direction of Py is expressed by the following equation (1) EQU .SIGMA..SIGMA..delta.(x-mPx, y-nPy) (1)
where x and y designate horizontal and vertical coordinates respectively and m and n are both integers.
The carrier component produced by such spatial sampling is expressed by Fourier-transforming Eq. (1) and is presented as ##EQU1## where represents the Fourier transform and u and v represent the horizontal and vertical spatial frequencies, respectively.
Accordingly, carrier components F.sub.R, F.sub.G and F.sub.B of the three primary color signals R, G and B produced when the color filter 3 shown in FIG. 1B is used are expressed by the following equations (3), (4) and (5), respectively. ##EQU2##
The exp (-jPxu) and exp (-j2Pxu) in the carrier components F.sub.G and F.sub.B represent phase differences relative to the carrier component F.sub.R, respectively.
If such carrier components are shown on the spatial spectrum, they become as shown in FIG. 2. In FIG. 2, the abscissa f.sub.x and the ordinate f.sub.y represent the horizontal and vertical frequencies that are normalized by Px/2.pi. and Py/2.pi., respectively. In the spatial spectrums, the length of the arrow represents the magnitude of the carrier component, and the direction of the arrow represents the phase difference among the carrier components.
From this spatial spectrums, it will be seen that in addition to the base band component with the position of (f.sub.x, f.sub.y)=(0, 0) as the center, the carrier components are produced respectively at the positions (f.sub.x, f.sub.y)=(1/3, 0), (2/3, 0), (1, 0), (0, 1/2), (0, 1) and so on as the center by the color separation sampling.
In the spatial spectrums of FIG. 2, there are only shown the carrier components which will cause the aliasing distortion and also the carrier components shown by broken lines if FIG. 2 are such ones which may be cancelled out by the electrical reading processing which will be described later.
The carrier components existing at the position of (1, 0) will cause a moire when an object with a narrow stripe pattern formed of black and white stripes extending in the vertical direction is picked up; the carrier components existing at the position of (2/3, 0) will cause a cross color which will present green and magenta colors when an object with a somewhat narrow longitudinal stripe pattern is picked up; and the carrier components existing at the position of (1/3, 0) will cause a cross color which will present green and magenta colors when an object with a little rough longitudinal stripe pattern is picked up.
In like manner, the carrier components existing at the position of (0, 1) will produce a moire when an object with a narrow horizontal stripe pattern is picked up, and the carrier components existing at the position of (0, 1/2) will cause a flicker to occur by the interlaced scanning when an object with a little rough horizontal stripe pattern is picked up.
In this case, however, the flicker caused by the carrier components existing at the position of (0, 1/2) can be electrically removed because the carrier components are cancelled out by reading out the CCD charge transfer device in the manner of a known field reading method (where two adjacent horizontal lines are read out simultaneously). For this reason, the quality of a picture is deteriorated mainly by the carrier components in the horizontal direction.
When a color filter of a pattern in which the color filter element of the primary color G is formed of longitudinal stripe and the color filter elements of the other primary colors R and B are formed of the color filter elements arranged in the line sequential manner is used as the color filter 3 shown in FIG. 1B, the fundamental lattice as shown in FIG. 3A is presented. As a result, the respective carrier components of the three primary colors R, G and B in the case of such color coding become as shown in FIG. 4 on the spatial spectrum.
Also in FIG. 4, there are shown the carrier components that are harmful for the signal processing, similarly to FIG. 2. The moire will be caused by particularly the carrier components existing at the positions of (f.sub.x, f.sub.y)=(1, 0) and (0, 1), while the cross color will be caused by the carrier components existing at the positions of (f.sub.x, f.sub.y)=(1/2, 0) and (0, 1/2). In the case of the color coding as shown in FIG. 3B, since the primary colors R and B are arranged in the line sequential manner, the signal charge can not be read out by the field reading manner unlike the above-described example. However, if the vertical interpolation is carried out by the signal processing system provided affer the sample-and-hold operation for color separation was carried out, the moire in the vertical direction can be reduced.
By the way, if the color filter 3 such as shown in FIG. 1B or 3B is used, the moire and the cross color are produced due to the carrier components of the three primary colors R, G and B particularly existing in the horizontal frequency f.sub.x direction. Therefore, in the prior art, an optical low pass filter is disposed in the optical system of the image pickup apparatus, whereby the spatial frequency response in the horizontal frequency is made as a low pass characteristic, thus the carrier components being suppressed.
As such prior art optical low pass filters, there are used such ones in which three crystal plates are laminated as disclosed in a published document of Japanese examined patent application No. 50336/1983 and a published document of Japanese unexamined patent application No. 39683/1982. In the prior art optical low pass filter disclosed in the published document of Japanese patent application examined No. 50336/1983 and in the prior art optical low pass filter disclosed in the published document of Japanese unexamined patent application No. 39683/1982, there are respectively provided the low pass characteristics shown in FIG. 12 and FIG. 17 thereof by properly selecting a projection angle relative to the horizontal scanning direction H and a separated distance d on the pickup surface at each optical axis thereof.
If the characteristic of the optical low pass filter is set as such optical low pass characteristic as described hereinabove, the carrier components existing at the positions after the position of (f.sub.x, f.sub.y)=(1/3, 0) are suppressed so that the occurrence of the moire and cross color can be reduced and the deterioration of the quality of picture can be improved.
By the way, such prior art optical low pass filters are formed by laminating three crystal plates. As is known, a crystal plate is very expensive, and when three crystal plates are laminated, they must be laminated under the condition that they are accurately positioned so as to make the projection angles of the optical axes equal to the designed values. This requires high accuracy in laminating the three crystal plates so that it is difficult to manufacture the optical low pass filter. Hence the yield thereof is considerably low and the workability thereof is poor.